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Probabilities

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1. This problem is in reference to students who may or may not take advantage of the opportunities provided in QMB such as homework. Some of the students pass the course, and some of them do not pass. Research indicates that 40% of the students do the assigned homework. Of the students who do homework, there is an 80% chance they will pass the course. The probability of not passing if the students does not do the homework is 90%. What is the probability of a student not doing homework or passing?

2. In a survey about soft drinks it was found that 5% of the respondents like diet soft drinks. 12% of the respondents like the brand Coke. Of the diet soda drinkers, 40% like Coke. What is the probability that a respondent did like diet drinks or did not like Coke?

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1. Probabilities given:
Candidates doing home work P(H) = 0.4
Candidates not doing homework P(NH) = 1.0 - 0.4 = 0.6

Candidates passed from group of doing home work P(P/H) = 0.8
Candidates not passed from group of not doing homework P(NP/NH) = 0.9

Calculations:
Probability of candidates passed who did assignment P(P AND H) = P(H) * P(P/H) = 0.4*0.8 = ...

Solution Summary

Probabilities are reiterated clearly.

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A young engineer has invented holographic mobile phones and has approached a venture capital company to invest in it. The venture capital company considers the product to be an all or nothing product: either everyone will want one because everyone else has one or no one will want one because there will be no one to use it with. The company believes that the probability that it will take off netting them a profit of $2000000 is 0.14. If it doesn't take off then they expect that they would loose $200000. They are considering using a consumer survey to gather more information. However, the company has experience that shows that the probability that the consumer survey will predict success for a product that will fail is 0.24, and the probability that the consumer survey will predict failure when the product will be a success is 0.07. What is the monetary value of the information from a consumer survey to the venture capital company in this case? (ie what is the maximum that they should spend on a consumer survey)?

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